Intrinsic Spin and Orbital Angular Momentum Hall Effect.

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Zhang, S. & Yang, Z., 2005. Intrinsic Spin and Orbital Angular Momentum Hall Effect. Phys. Rev. Lett. 94, 066602

Essay about this article

The ordinary Hall effect was discovered in 1879 by Edwin Hall. It refers to the difference in potential produced on the opposite sides of a conductor when a current is flowing in the presence of a magnetic filed applied perpendicular to the current. The effect arises from the Lorentz force acting on a moving charge in a magnetic field that curves its trajectory away from its straight-line path. This causes charge to accumulate [pile up] on one side of a conductor and create a potential difference across the opposite sides of a conductor. If one connects the sides to another conductor, a current transverse to the initial current flows though it, which is called a Hall current. In this way the Hall effect is viewed as a source for transverse electromotive force (EMF), a kind of generator.

In the late 1950’s there was a flurry of theoretical interest to place one’s understanding of this effect on firm quantum mechanical grounds; as it turned out this lead to a rather acrimonious debate between Jan Smit of Holland and J.M. (Quin) Luttinger of Columbia University in New York. Both considered other origins for the Hall effect which included the asymmetric scattering [known as skew scattering] from impurities with spin-orbit coupling and a more esoteric quantum mechanical effect arising from the time delay in scattering events that in the presence of spin-orbit scattering produced a “side jump”, i.e., when one traced the path of a scattered electron back to the scattering region it was displaced to one side of the scattering center.[1] The debate was over which mechanism was responsible for the additional Hall voltage observed in conductors with ferromagnetic scattering centers. It was resolved in the early 1960’s, and both sides were right. There are indeed two different manifestations of spin-orbit scattering contributing to the additional Hall effects [called the extraordinary Hall effect]. The first is skew scattering, and the second is the side jump which arises not only from spin-orbit scattering off impurities, but also from ordinary [charge] scattering when the electron conduction wavefunctions have their spin and orbit coupled together.

In the 1970’s Albert Fert studied the extraordinary effect in ferromagnetic metals, and became an established authority on the effect. At the time of the centennial celebration at Johns Hopkins University, where Hall discovered the effect, Dr. Fert was an invited speaker. Together we studied in the early 1980’s the role of skew scattering and the side jump in scattering from Kondo impurities [2] in metals.

By way of this extensive introduction, fast-forward to 1999 when Jorge Hirsch introduced the concept of the spin Hall effect; this refers to the accumulation of spin, rather than charge, at opposite sides of a conductor arising from spin-orbit scattering that has electrons scatter to the right or left of impurities depending on the orientation of their spin. Notably, it does not require an applied magnetic field. This effect was first suggested by Neville Mott. One way of producing a spin-polarized beam of electrons is by spin-orbit scattering an unpolarized beam off a gold target: because of its high atomic number gold has a good spin-orbit scattering cross-section. The device is called a Mott spin detector.

Shufeng Zhang provided a realistic assessment of the spin Hall effect that provided valuable guidance for experimentalists. By 2004-05 the effect was observed by two groups, Awschalom’s and Wunderlich’s; while the first group attributed the spin accumulation to the spin accumulation attendant to spin-orbit scattering of a current, the latter raised the possibility that what they were observing was an effect that had little dependence on the impurity scattering. Wunderlich observed, “Microscopic quantum transport calculations show only a weak effect of disorder, suggesting that the clean limit spin-Hall conductance description (intrinsic spin-Hall effect) might apply to our system.” This set off a new flurry of theoretical activity by Sinova, Nagaosa, and Shoucheng Zhang to find markers for the extrinsic [impurity driven] and intrinsic [an equilibrium effect independent of scattering off defects] spin Hall effects. It was shown that the latter, the intrinsic spin Hall effect, has a “universal” conductivity; this is its signature. A debate ensued of how one would be able to observe this intrinsic effect, and Shufeng Zhang weighed in by remarking that in contradistinction to the extrinsic effect there is no detectable spin accumulation associated with the intrinsic spin Hall effect. Entering the discussion was also the question as to what constitutes the correct description of a spin current when spin-orbit coupling is present. Shufeng showed that an orbitally polarized current is also present; in the intrinsic limit this exactly cancelled the effect of the spin polarized current. At the present time it seems to me the observation of the intrinsic spin Hall effect is an open question.


[1] This beautiful explanation of side-jump arising from time delay in the presence of spin-orbit scattering was developed by Luc Berger in the 1970’s. See L. Berger, Phys. Rev. B 2, 4559 (1970), and articles by Berger, G. Bergmann and C.M. Hurd in, The Hall Effect and Its Applications, C.L. Chien and C.R. Westgate, Eds. (Plenum, New York, 1980).

[2 ]The Kondo effect refers to an instability at the Fermi surface of metals induced by exchange scattering off magnetic impurities, which produces a tiny gap in the spin density of states around the Fermi level; see J. Kondo Solid State Physics, Vol. 23, edited by F. Seitz, D. Turnbull and H. Ehrenreich (Academic Press, New York, NY.,1969).

See Also:

Dissipationless Quantum Spin Current at Room Temperature. Science 301, 1348 (2003). Article available from Science in full text after free registration

J.E. Hirsch, Phys. Rev. Lett. 83, 1834 (1999);

S. Zhang, Phys. Rev. Lett. 85, 393 (2000);

Y. K. Kato, R. C. Myers, A. C. Gossard, D. D. Awschalom, Science 306,1910(2004);

J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. MacDonald, Phys. Rev. Lett. 92, 126603 (2004);

J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, Phys.Rev.Lett. 94, 047204 (2005);

S. Zhang and Z. Yang, Phys. Rev. Lett. 94, 066602 (2005).

Discussion Question

The mechanisms that produce the spin Hall effect were studied several decades before the effect was called the “spin Hall effect”. Under what name was it known before, and opine why it was renamed?

The above article is reprinted with permission from the author(s) of Zhang, S. & Yang, Z., 2005. Intrinsic Spin and Orbital Angular Momentum Hall Effect. Phys. Rev. Lett. 94, 066602. Copyright (2005) by the American Physical Society. Readers may view, browse, and/or download material for temporary copying purposes only, provided these uses are for noncommercial personal purposes. Except as provided by law, this material may not be further reproduced, distributed, transmitted, modified, adapted, performed, displayed, published, or sold in whole or part, without prior written permission from the American Physical Society .

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Rodina, A. V. and A. Y. Alekseev (2008). "Theory of intrinsic electric polarization and spin Hall current in spin-orbit-coupled semiconductor heterostructures." Physical Review B 78(11).

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Culcer, D. (2008). "STEADY-STATE SPIN DENSITIES AND CURRENTS." International Journal of Modern Physics B 22(27): 4765-4791.

Tse, W. K. and S. Das Sarma (2006). "Spin Hall effect in doped semiconductor structures." Physical Review Letters 96(5).

Shi, J. R., P. Zhang, et al. (2006). "Proper definition of spin current in spin-orbit coupled systems." Physical Review Letters 96(7).

Sun, Q. F. and X. C. Xie (2005). "Definition of the spin current: The angular spin current and its physical consequences." Physical Review B 72(24).

Nikolic, B. K., L. P. Zarbo, et al. (2005). "Mesoscopic spin Hall effect in multiprobe ballistic spin-orbit-coupled semiconductor bridges." Physical Review B 72(7).

Nikolic, B. K., S. Souma, et al. (2005). "Nonequilibrium spin hall accumulation in ballistic semiconductor nanostructures." Physical Review Letters 95(4).

Bernevig, B. A. and S. C. Zhang (2005). "Intrinsic spin hall effect in the two-dimensional hole gas." Physical Review Letters 95(1).

Adagideli, I. and G. E. W. Bauer (2005). "Intrinsic spin Hall edges." Physical Review Letters 95(25).

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